Physics Question on Ray optics and optical instruments

Question

A concave lens of focal length 20 cm produces an image half the size of the real object. The distance of the real object is

Answer 1

Solution

From lens formula
$\frac{1}{f}= \frac{1}{v}= \frac{1}{u}$
Given, $v = \frac{u}{2}$ and $f=20\, cm$
$\Rightarrow \frac{1}{20}= \frac{1}{u/2}= \frac{1}{u}= \frac{1}{u}$
$\Rightarrow u = 20\, cm$